{"paper":{"title":"Model completeness and relative decidability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jennifer Chubb, Reed Solomon, Russell Miller","submitted_at":"2019-03-02T16:52:22Z","abstract_excerpt":"We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model $\\mathcal A$ of a computably enumerable, model complete theory, the entire elementary diagram $E(\\mathcal A)$ must be decidable. We prove that indeed a c.e. theory $T$ is model complete if and only if there is a uniform procedure that succeeds in deciding $E(\\mathcal A)$ from the atomic diagram $\\Delta(\\mathcal A)$ for all countable models $\\mathcal A$ of $T$. Moreover, if every presentation of a single isomorphism type $\\mathc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00734","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}